Question

the side of a square is 2 cm its perimeter is 8 cm plot graph of perimeter versus side of the square show the following on the graph.

a) the perimeter of the square when side is 4 cm

b) the side of the square one parameter is 12 CM ​

Answer 1

It is given that AB is the chord of the circle with centre O.

Now

$\sf\red{OP \perp AB}$

Therefore,OP bisects AB.

AL = BL = 8cm

Also,

$\sf\red{OL = √ {OA}^{2} - {AL}^{2} = √{10}^{2} - {8}^{2}=√36 = 6cm}$

Now,

$\sf\red{\angle PAL = \angle OAL = 90°}$ (tangent is perpendicular to the radius through the point of contact)

$\sf\red{\angle PAL = \angle APL= 90°}$ (sum of angles in ∆APL is 180.

$\sf\red{\angle PAL + \angle OAL }$

Now,in ∆APL & ∆OAL,

$\sf\red{\angle PLA = \angle OLA(90°\:each)}$

$\sf\red{\angle APL = \angle OLA (proved) }$

$\sf\red{\therefore ∆APL ~ ∆OAL( AA similarity)}$

$\sf\red{PA = AL}$

$\sf\red{OA = OL}$(corresponding sides are proportional) }[/tex]

$\sf\red{PA = \frac{40}{3}cm}$

$\sf\red{40}$

Thus, the length of the tangent PA is 40.

Answer 2

We know that the perimeter of a square is four times of its side. (i.e) P = 4a. 

(Here, P = Perimeter and a = side) 

For different values of a, the values of P are given in the following table. 

a (in cm) 1234P = 4a (in cm)481216Points: (1, 4), (2, 8), (3, 12), (4, 16). 

Plot the above points. Join all the points. We get the linear graph of P = 4a.